For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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1answer
32 views

Uniform distribution of points on an n-sphere

Is it possible to evenly distribute N=5 points on a 3-sphere such that: the distance between any two points is equal. the points are all distinct. in complete analogy to the even distribution of 4 ...
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2answers
103 views

The area of the region $|x-ay| \le c$ for $0 \le x \le 1$ and $0 \le y \le 1$

What is the area of the following region: $|x-ay| \le c$ for $0 \le x \le 1$ and $0 \le y \le 1$. Assume $c>0$. We can also assume $|a|>1$ since it will not change the essence of the ...
2
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2answers
78 views

Drawing the region which the pedestrian can cover in 1 hour.

A straight path separates a meadow from a field. A pedestrian travels along the path at a speed of 5 km/hr, through the meadow at a speed of 4 km/hr, and through the field at a speed of 3 ...
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1answer
23 views

Packing of rectangular blocks

There are 3 cubes side length of each a, b and c. There are also 3 identical rectangular blocks with sides measuring (a + b ), (b + c) and (c + a ). Can they be assembled together to form a cube of ...
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2answers
23 views

Equations of a projective variety from parametric ones

How does one find equations of a variety given parametric equations (i.e. a regular map) in projective space? For example, I got stuck in finding the equations of the curve in $\Bbb{P}^2$ described by ...
2
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1answer
46 views

Intersection of nested closed bounded convex sets in Euclidean space

I read that in a complete Euclidean space - i.e. a normed real space with the norm induced by the scalar product - any sequence of nested bounded non-empty closed convex sets has a non-empty ...
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0answers
27 views

how to hinge-dissect an 1-omino to 3-omino?

Recently I am doing a project about hinge-dissection of poly-omino. A poly-omino is a finite collection of copies of a identical squares such that the interior of their union is connected, and the ...
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3answers
145 views

Is Adobe Acrobat's icon a special function?

It looks like a function in polar coordinates. Is it a special function ?
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1answer
30 views

Transformation matrix from a translated-rotated coordinate system to the general coordinate system

In Figure 1, suppose $XYZ$ (in black) as my general coordinate system and $X'Y'Z'$ (orange) as another system with parallel axes respect to $XYZ$. Consider $xyz$ (green) is my 3rd coordinate system ...
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2answers
56 views

Area remaining after maximal number of tiles are laid on a pathway

A rectangular plot measuring $30$ m $\times$ $40$ m has a $2$ m wide pathway in the middle crosswise. Tiles of dimensions $30$ cm $\times$ $50$ cm are laid on the pathway in such a way so that no ...
3
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0answers
28 views

Help me visualize seven maximally-spaced points on a sphere

I'm interested in the subject of maximally separated points (e.g., the minimum of the distances between any two of the points is maximal) in various spaces, and I've been trying to think about how ...
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0answers
26 views

Generalized Mass Points

Is there a generalized algebraic structure for the set of mass points under addition? Mass points are points in the plane with assigned masses, so that addition gives the center of mass between any ...
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2answers
61 views

Rotate secondary vanishing points to the primary vanishing points to find new length of object

all though only the 2D data is available, the best way to think of this problem is a piece of paper pinned at one corner to a wall, but the paper is sitting at an angle to the wall, see illustration ...
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0answers
42 views

Finding circle which touches two functions

I wasn't sure whether my issue is with my Mathematica code or the actual way I am trying to figure out my problem so if it is a Mathematica issue I can ask it on that stack exchange. Firstly I have ...
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1answer
46 views

Center of a circumference?

Does the circumference have a center?, I mean the center of a triangle is a point in the triangle that will always occupy the same position under the operations of rotation, reflection, and dilation ...
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3answers
27 views

Find the measure of angle E.

http://static.k12.com/eli/bb/811/7537/0/2_36640_44211/7537/cfcbab7622b25115e3996826ebe54350776a6601/media/a0fb44a9ac3761c0d89bd1c3ffa513c508eb78bf/mediaasset_650483_1.gif help please i still mix the ...
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1answer
44 views

Is $\sin \theta_{xy}\leq \sin \theta_{xz}+\sin\theta_{yz}$, where $\theta_{ab}$ is angle between unit vectors $a$ and $b$?

Suppose $x,y,z\in\mathbb{R}^n$ are unit vectors. The angle between unit vectors $a$ and $b$ is $\theta_{ab}=\arccos(a\cdot b)$ where $a\cdot b$ is the dot-product. Is $\sin \theta_{xy}\leq \sin ...
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2answers
49 views

Find the value of $a$.

please help I'm lost on what numbers to add or what formula to use
1
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1answer
21 views

How to calculate the radial cross section of a torus depending on a certain angle?

Imagine a torus, I cutted in half: It is quite easy to calculate the red area: $$A_1(\alpha=0) = \pi ( R+r)^2 - \pi R^2$$ as well as the green area: $$A_1(\alpha=\frac{\pi}{2}) = 2\pi R \cdot ...
3
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1answer
43 views

Who first proved that every triangle has a circumscribed circle?

Wikipedia only mentions that it follows from the Cartesian equation for a circle: $\left(x - a \right)^2 + \left( y - b \right)^2=r^2$ https://en.wikipedia.org/wiki/Circumscribed_circle#cite_note-1 ...
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0answers
33 views

Finding the geographical coordinates

I have two circles $C_1$ and $C_2$ on the surface of the earth (sphere) intersecting at geographical coordinates $A$ and $B$ and also center of $C_1$ lies in $C_2$ and vice versa. I want to find the ...
0
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1answer
33 views

Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
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0answers
119 views

Which power means are constructible?

The three classic Pythagorean means $A$, $G$, $H$ (arithmetic, geometric, and harmonic mean respectively) of positive real $a$ and $b$ have a cute geometric construction, as does the quadratic mean ...
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3answers
158 views

Why isn't the volume of a sphere $ π^2r^3?$

Imagine two similiar circles. We rotate one on half of the other circumference. It gives a sphere with volume of $1/2(2πr) \cdot πr^2 = π^2r^3$
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2answers
48 views

Intersection of circle and ellipse

I'm looking for the points of intersection of a circle $x^2 + y^2 = r^2$ ($r$ is known, origin is $(0,0)$) and an ellipse $(x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 = 1$ ($a,b,x_0,y_0$ are known). ...
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0answers
75 views

Understanding the Banach-Tarski Paradox

How is it possible to prove a paradox? Also, can someone explain the Banach-Tarski paradox in layman's terms (for someone up to calc 3 and ODEs knowledge)?
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1answer
94 views

The minimum number of circles in order to obtain a COVER of a specific square

Suppose a unit square $X$, with side length $l=1$ as below, which is COVERed by a set $Y$ of circles with the same constant radius of $r=\dfrac{\sqrt{2}}{10}$, where a ...
1
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1answer
38 views

How to prove that this geometric constructions for the pythagorean means are right?

According to wikipedia the Pythagorean means (and the quadratic one) of two numbers can be constructed geometrically in this way: While the arithmetic mean it's obvious, and I think I understood the ...
1
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2answers
28 views

Geometry, finding the possible values of 'a'

$P (a,4)$, $Q (2,3)$, $R (3,-1)$ and $S (-2,4)$ are four points. If $|PQ| = |RS|$, find the possible values of a I know this is a pretty basic problem but I'm having a lot of trouble with it, here is ...
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0answers
30 views

Other notions of “dimension”?

Beyond that topological notion of "dimension" are there others that are common in mathematics/physics? Thus far, I know of the Hausdorff and spectral dimensions.
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1answer
53 views

I need to find the value of x. Im only given the a degree how would you solve this?

this is the link to the triangle that is connected to the question. What is the value x?
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0answers
14 views

How can the R3 vertices of a 4-dimensional object be generated?

After learning a bit of OpenGL, I was hoping to find a way to project a 4-dimensional object into 3-space to visually study them. However, I'm not even sure how I would begin to do this. What kind ...
1
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3answers
30 views

Calculating the angle for a path between two nodes in a graph

I want to (programatically) draw an edge between two nodes in a graph, starting on the outside of the nodes. Below is an illustration of what I'm (poorly) trying to describe: I have the $(x,y)$ ...
0
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1answer
23 views

Compute the isotropy representation

Suppose $SU(1,1)$ acts on the open unit disc $\mathbb{D}$ in the natural way, by linear fractional transformations. The isotropy group is $U(1),$ since it stabilizes the point $0.$ I am trying to ...
2
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1answer
32 views

Do the medians (or other cevians) form all the triangles?

I want to know whether set of medians of all triangles, or some other class of cevians, can form the set of all the triangles? For example, in the case of altitudes, $(4,7,10)$ is an counterexample. ...
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2answers
31 views

How to find if a point lies in the area covered by 2 straight lines

Given 2 lines Y1 = m1X1 + C1 Y2 = m2X2 + C2 Now given a point (X3,Y3), how will one find whether the point lies in the area enclosed by the 2 straight lines? In ...
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0answers
27 views

Predicting Bending of Plywood (Conical Shapes)

I'm building a NASCAR-style banked track for 1/27 scale RC cars, and I'm trying to predict the bends I need to cut to produce the banked track I want. I've already built some simple banked pieces, ...
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2answers
22 views

Rotate and translate a line so that it passes through two given points

I have 2 point and a line segment in 2d space. The line only rotates and translates using its mid point. How do I calculate the translation and rotation required for the line to be touching the 2 ...
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0answers
17 views

Sphere degenerates to point in discrete space?

Is it - or can it be - correct to say that a sphere degenerates into a point in discrete space? When I say "degenerate", I mean in the same way a torus can degenerate into a sphere. I specify a ...
0
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0answers
28 views

Volume of a rotated regular polygon

I want to calculate the volume of the shape which is created when you rotate a regular $n$-sided polygon around the $y$ axis with a major radius $r$. (like a torus, but with a polygon as rotated ...
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2answers
134 views

Finding equation of an ellipsoid

Consider I have an ellipsoid (let say an egg) lies in a general form in 3D space. Suppose, I have the equations of two projected views of this egg (e.g. one projected view on x-y plane and another one ...
0
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2answers
48 views

Simple geometry problem

So I'm asking this question because I'm afraid I would be doing a stupid mistake... the problem associated with this trigonometry problem isn't pulling off. Could you tell me whether my calculation is ...
1
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1answer
66 views

Find r in terms of theta

I have been given the following question: My answer for question a) is $\theta/(2\pi)$. The books answer is $(2\pi-theta)/(2\pi)$. I came to my answer by calculating the arc length of the sector ...
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0answers
30 views

Mathematically creating a scale model of a tank

I am having a difficult time solving the following question: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension ...
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2answers
42 views

Representing 2D objects in 4D

What is the general quation of a 2D object, e.g. a surface in 4D? I read, that while a line is representable in 2D using the general equation of degree one ($ax + by + c = 0$), in 3D, one needs a ...
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0answers
59 views

Hypervolume of expanded $n$-simplex

The hypervolume of the expanded $n$-simplex with side $\sqrt{2}$ appears to be $$\displaystyle\frac{\sqrt{\;n+1\;}\;(2n)!}{n!^3}$$ Does anyone know of a published reference to this result? An ...
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0answers
25 views

Slicing through a cuboid containing spheres, how many are exposed to the surface and what is their combined volume

So I place spheres of radius chosen at random from a normal distribution of known mean and standard deviation in a cub or cuboid at random (not overlapping) until a known density of the entire cube is ...
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0answers
28 views

Help understanding Archimedes method for finding the area of a circle

I'm struggling to understand the method described on this page http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/integration/archimedes.html specifically step 1, I can't replicate how they have ...
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1answer
27 views

Proof with parallelogram inside a parallelogram

Prove that $PBRS$ is a parallelogram. (Note: $P$ and $Q$ are respectively the middles of the sides $AB$ and $CD$) Now the corrections give the following method: $PBQD$ is a parallelogram $BR ...
2
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1answer
27 views

Surface of 3D Triangle

The coordinates $A(-1,0,2), B(2,-1,3)$ and $C(4,0,1)$ are the corners in the triangle $ABC$. a) Find the length of the sides in the triangle. b) Find the area of the triangle. Now I'm able to ...